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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 259 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
543.1.z.a	$543$	$1$	543.z	543.z	$30$	$8$	$1$	$0.271$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{4}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{9}+\cdots)q^{7}+\cdots$
651.1.ch.a	$651$	$1$	651.ch	651.bh	$30$	$8$	$1$	$0.325$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q+\zeta_{30}^{11}q^{3}-\zeta_{30}^{13}q^{4}-\zeta_{30}^{12}q^{7}+\cdots$
651.1.co.a	$651$	$1$	651.co	651.bo	$30$	$8$	$1$	$0.325$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-1$	$1$		$q-\zeta_{30}^{9}q^{3}-\zeta_{30}^{7}q^{4}+\zeta_{30}q^{7}-\zeta_{30}^{3}q^{9}+\cdots$
732.1.bm.a	$732$	$1$	732.bm	183.v	$30$	$8$	$1$	$0.365$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$5$	$1$		$q+\zeta_{30}^{6}q^{3}+(\zeta_{30}^{5}+\zeta_{30}^{8})q^{7}+\zeta_{30}^{12}q^{9}+\cdots$
775.1.z.b	$775$	$1$	775.z	775.z	$10$	$8$	$2$	$0.387$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$5$	$0$	$-1$	$0$	$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{10})q^{2}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
792.1.cl.a	$792$	$1$	792.cl	792.bl	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{30}^{7}q^{2}-\zeta_{30}^{4}q^{3}+\zeta_{30}^{14}q^{4}+\cdots$
792.1.cl.b	$792$	$1$	792.cl	792.bl	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{30}^{7}q^{2}+\zeta_{30}^{13}q^{3}+\zeta_{30}^{14}q^{4}+\cdots$
837.1.bo.a	$837$	$1$	837.bo	31.h	$30$	$8$	$1$	$0.418$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+\zeta_{30}^{9}q^{4}+(\zeta_{30}^{2}+\zeta_{30}^{6})q^{7}+(-\zeta_{30}^{2}+\cdots)q^{13}+\cdots$
915.1.cm.a	$915$	$1$	915.cm	915.bm	$30$	$8$	$1$	$0.457$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$-2$	$-1$	$0$	$1$		$q+(\zeta_{30}-\zeta_{30}^{13})q^{2}+\zeta_{30}^{12}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
915.1.cm.b	$915$	$1$	915.cm	915.bm	$30$	$8$	$1$	$0.457$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$2$	$1$	$0$	$1$		$q+(-\zeta_{30}+\zeta_{30}^{13})q^{2}-\zeta_{30}^{12}q^{3}+\cdots$
943.1.k.b	$943$	$1$	943.k	943.k	$10$	$8$	$2$	$0.471$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(\zeta_{30}^{5}+\zeta_{30}^{13})q^{2}+(\zeta_{30}^{7}+\zeta_{30}^{8}+\cdots)q^{3}+\cdots$
964.1.ba.a	$964$	$1$	964.ba	964.aa	$30$	$8$	$1$	$0.481$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$4$	$0$	$-2$	$0$	$1$		$q+\zeta_{30}^{5}q^{2}+\zeta_{30}^{10}q^{4}+(\zeta_{30}^{7}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
976.1.cp.a	$976$	$1$	976.cp	244.v	$30$	$8$	$1$	$0.487$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$6$	$0$	$1$		$q+(\zeta_{30}^{5}+\zeta_{30}^{9})q^{5}+\zeta_{30}^{12}q^{9}+(-\zeta_{30}^{7}+\cdots)q^{13}+\cdots$
987.1.o.c	$987$	$1$	987.o	987.o	$6$	$8$	$4$	$0.493$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-3$	$1$	$0$	$-1$	$1$		$q+(\zeta_{30}-\zeta_{30}^{9})q^{2}-\zeta_{30}^{7}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
987.1.o.d	$987$	$1$	987.o	987.o	$6$	$8$	$4$	$0.493$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$3$	$-1$	$0$	$-1$	$1$		$q+(\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+\zeta_{30}^{7}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots$
1023.1.dk.a	$1023$	$1$	1023.dk	1023.ck	$30$	$8$	$1$	$0.511$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$-3$	$0$	$1$		$q-\zeta_{30}^{14}q^{3}+\zeta_{30}^{3}q^{4}+(-\zeta_{30}^{9}+\cdots)q^{5}+\cdots$
1023.1.dk.b	$1023$	$1$	1023.dk	1023.ck	$30$	$8$	$1$	$0.511$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$3$	$0$	$1$		$q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{3}q^{4}+(\zeta_{30}^{9}-\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
1027.1.s.b	$1027$	$1$	1027.s	1027.s	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}+\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1100.1.cd.a	$1100$	$1$	1100.cd	275.s	$10$	$8$	$2$	$0.549$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(-\zeta_{30}-\zeta_{30}^{2})q^{3}-\zeta_{30}^{10}q^{5}+\cdots$
1116.1.ck.a	$1116$	$1$	1116.ck	31.h	$30$	$8$	$1$	$0.557$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{11})q^{7}+(-\zeta_{30}^{12}+\zeta_{30}^{14}+\cdots)q^{13}+\cdots$
1159.1.cj.a	$1159$	$1$	1159.cj	1159.bj	$30$	$8$	$1$	$0.578$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$-3$	$1$		$q+\zeta_{30}^{13}q^{4}+(\zeta_{30}^{7}+\zeta_{30}^{9})q^{5}+(\zeta_{30}+\cdots)q^{7}+\cdots$
1195.1.c.e	$1195$	$1$	1195.c	1195.c	$2$	$8$	$8$	$0.596$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{11})q^{2}+(-\zeta_{30}^{6}-\zeta_{30}^{9}+\cdots)q^{3}+\cdots$
1209.1.dp.a	$1209$	$1$	1209.dp	1209.cp	$30$	$8$	$1$	$0.603$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-3$	$1$		$q-\zeta_{30}^{12}q^{3}+\zeta_{30}q^{4}+(-\zeta_{30}^{3}-\zeta_{30}^{4}+\cdots)q^{7}+\cdots$
1209.1.dr.a	$1209$	$1$	1209.dr	1209.cr	$30$	$8$	$1$	$0.603$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{30}^{4}q^{3}+\zeta_{30}^{7}q^{4}+(\zeta_{30}^{11}-\zeta_{30}^{13}+\cdots)q^{7}+\cdots$
1220.1.ck.a	$1220$	$1$	1220.ck	1220.bk	$30$	$8$	$1$	$0.609$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-4$	$0$	$1$		$q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{10}q^{5}+\cdots$
1220.1.ck.b	$1220$	$1$	1220.ck	1220.bk	$30$	$8$	$1$	$0.609$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}-\zeta_{30}^{3}q^{5}+\cdots$
1220.1.ck.c	$1220$	$1$	1220.ck	1220.bk	$30$	$16$	$2$	$0.609$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{60}^{7}q^{2}+(\zeta_{60}^{25}-\zeta_{60}^{29})q^{3}+\cdots$
1271.1.bg.b	$1271$	$1$	1271.bg	1271.ag	$10$	$8$	$2$	$0.634$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$2$	$-5$	$1$		$q+(\zeta_{30}^{7}-\zeta_{30}^{14})q^{2}+(\zeta_{30}^{6}-\zeta_{30}^{13}+\cdots)q^{4}+\cdots$
1281.1.cz.a	$1281$	$1$	1281.cz	1281.bz	$30$	$8$	$1$	$0.639$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q-\zeta_{30}^{11}q^{3}-\zeta_{30}^{12}q^{4}-\zeta_{30}^{3}q^{7}+\cdots$
1281.1.do.a	$1281$	$1$	1281.do	1281.co	$30$	$8$	$1$	$0.639$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$4$	$1$		$q-\zeta_{30}^{11}q^{3}+\zeta_{30}^{7}q^{4}+\zeta_{30}^{5}q^{7}+\cdots$
1300.1.cp.a	$1300$	$1$	1300.cp	1300.bp	$30$	$8$	$1$	$0.649$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}-\zeta_{30}q^{5}-\zeta_{30}^{6}q^{8}+\cdots$
1300.1.cp.b	$1300$	$1$	1300.cp	1300.bp	$30$	$8$	$1$	$0.649$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+\zeta_{30}^{2}q^{2}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{11}q^{5}+\cdots$
1316.1.j.c	$1316$	$1$	1316.j	1316.j	$6$	$8$	$4$	$0.657$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$-2$	$0$	$1$	$1$		$q+\zeta_{30}q^{2}+(\zeta_{30}^{7}+\zeta_{30}^{13})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1316.1.j.d	$1316$	$1$	1316.j	1316.j	$6$	$8$	$4$	$0.657$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$2$	$0$	$-1$	$1$		$q-\zeta_{30}^{6}q^{2}+(-\zeta_{30}^{7}-\zeta_{30}^{13})q^{3}+\cdots$
1339.1.t.b	$1339$	$1$	1339.t	1339.t	$6$	$8$	$4$	$0.668$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q+(-\zeta_{30}^{2}+\zeta_{30}^{8})q^{2}+(-\zeta_{30}+\zeta_{30}^{4}+\cdots)q^{4}+\cdots$
1395.1.dw.a	$1395$	$1$	1395.dw	155.v	$30$	$16$	$2$	$0.696$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{60}^{7}+\zeta_{60}^{11})q^{2}+(\zeta_{60}^{14}+\zeta_{60}^{18}+\cdots)q^{4}+\cdots$
1463.1.ds.a	$1463$	$1$	1463.ds	1463.cs	$30$	$8$	$1$	$0.730$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$3$	$-4$	$1$		$q+\zeta_{30}q^{4}+(-\zeta_{30}+\zeta_{30}^{3})q^{5}-\zeta_{30}^{5}q^{7}+\cdots$
1463.1.ds.b	$1463$	$1$	1463.ds	1463.cs	$30$	$8$	$1$	$0.730$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$3$	$-1$	$1$		$q+\zeta_{30}q^{4}+(-\zeta_{30}^{6}-\zeta_{30}^{13})q^{5}+\cdots$
1475.1.h.b	$1475$	$1$	1475.h	1475.h	$10$	$8$	$2$	$0.736$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$5$	$1$	$0$	$1$		$q+(\zeta_{30}^{5}-\zeta_{30}^{13})q^{3}+\zeta_{30}^{9}q^{4}-\zeta_{30}^{11}q^{5}+\cdots$
1488.1.dc.a	$1488$	$1$	1488.dc	372.ac	$30$	$8$	$1$	$0.743$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{30}^{14}q^{3}+(\zeta_{30}^{8}+\zeta_{30}^{11})q^{7}+\cdots$
1488.1.dc.b	$1488$	$1$	1488.dc	372.ac	$30$	$8$	$1$	$0.743$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{30}^{14}q^{3}+(-\zeta_{30}^{8}-\zeta_{30}^{11})q^{7}+\cdots$
1623.1.ba.a	$1623$	$1$	1623.ba	1623.aa	$30$	$8$	$1$	$0.810$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{30}^{2}q^{3}+\zeta_{30}^{11}q^{4}+(\zeta_{30}-\zeta_{30}^{2}+\cdots)q^{7}+\cdots$
1647.1.ch.a	$1647$	$1$	1647.ch	183.v	$30$	$8$	$1$	$0.822$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{30}^{11}q^{4}+(\zeta_{30}^{5}-\zeta_{30}^{9})q^{7}+(-\zeta_{30}^{8}+\cdots)q^{13}+\cdots$
1651.1.s.b	$1651$	$1$	1651.s	1651.s	$6$	$8$	$4$	$0.824$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-127}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{30}^{6}+\zeta_{30}^{14})q^{2}+(\zeta_{30}^{5}+\zeta_{30}^{12}+\cdots)q^{4}+\cdots$
1672.1.cn.a	$1672$	$1$	1672.cn	1672.bn	$30$	$8$	$1$	$0.834$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-3$	$0$	$0$	$1$		$q+\zeta_{30}q^{2}+(\zeta_{30}^{12}-\zeta_{30}^{14})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1672.1.cn.b	$1672$	$1$	1672.cn	1672.bn	$30$	$8$	$1$	$0.834$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-3$	$0$	$0$	$1$		$q-\zeta_{30}q^{2}+(-\zeta_{30}^{2}-\zeta_{30}^{9})q^{3}+\zeta_{30}^{2}q^{4}+\cdots$
1692.1.l.c	$1692$	$1$	1692.l	1692.l	$6$	$8$	$4$	$0.844$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$-2$	$0$	$3$	$1$		$q-\zeta_{30}^{8}q^{2}-\zeta_{30}^{9}q^{3}-\zeta_{30}q^{4}-\zeta_{30}^{2}q^{6}+\cdots$
1692.1.l.d	$1692$	$1$	1692.l	1692.l	$6$	$8$	$4$	$0.844$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$1$	$2$	$0$	$-3$	$1$		$q-\zeta_{30}^{11}q^{2}-\zeta_{30}^{12}q^{3}-\zeta_{30}^{7}q^{4}+\cdots$
1703.1.i.b	$1703$	$1$	1703.i	1703.i	$6$	$8$	$4$	$0.850$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{3}-\zeta_{30}^{10}q^{4}+(-\zeta_{30}^{7}+\cdots)q^{5}+\cdots$
1705.1.ek.b	$1705$	$1$	1705.ek	1705.dk	$30$	$8$	$1$	$0.851$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{30}^{2}-\zeta_{30}^{14})q^{3}+\zeta_{30}^{9}q^{4}-\zeta_{30}^{8}q^{5}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.